Abstract
The object of the present paper is to study the delay differential equation of arbitrary order namely y(n)(t) + a(t)yτ(t) = f(t), n≥2 (an integer) and prove a nonoscillation theorem under the general situation in which a(t) and f(t) are allowed to oscillate arbitrarily often on some positive half real line. This is accomplished by way of two differential inequalities of nth order.
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